A novel mesh deformation algorithm for general meshes is developed utilizing a tree-code optimization of a simple direct interpolation method. The algorithm is shown to provide competitive mesh quality with radial basis function based methods while showing markedly better performance in preserving boundary layer orthogonality in viscous meshes. The parallelization of the algorithm is described and the algorithm cost is demonstrated to be O(n log n). The parallel implementation was used to deform meshes of 100 million cells on nearly 200 processors showing the method scales to large mesh sizes. Results for a simulation of high Reynolds number fluid structure interaction case using this technique is provided.